1. Field of the Invention
The present invention relates to a spread spectrum signal generation method of and a spread spectrum signal generator for generating a chaos sequence as a spread spectrum signal.
The invention also relates to a stream encryption method where stream encryption is performed by using a binary code sequence according to the method and the generator.
The invention relates further to a stream enciphered codes communication method where communication is performed by using a cipher code obtained by the stream encryption method.
2. Description of the Related Art
As the digital high-speed communication spreads, it is desirable to implement a code division multiple access (CDMA) communication system using a spread spectrum communication system. In this field of endeavor, a binary number sequence generated by tossing a coin, is considered ideal as a spread spectrum signal (hereinafter called xe2x80x98SS signalxe2x80x99).
In conventional application to the spread spectrum communication system, a sequence obtained by cutting, in suitable length, a maximum length sequence, a Kasami sequence, Gold sequence or the like, is used as the SS signal. A maximum length sequence generated from multi-staged shift registers is also used.
However, conventional spread spectrum code sequences to be used conventionally as SS signal are limited in kinds, and may be insufficient to cope with expectable future demands for communications.
For example, for a sufficient secrecy to be secured for communications, it is necessary to avoid a so-called see-through state of an original text. To be so, an SS signal having a periodical temporal sequence suppressed of auto-correlation as well as of cross-correlation is desirable. It however is difficult for the conventional concept of generation to provide a periodical temporal sequence suppressed in auto-correlation and cross-correlation, with a good repeatability.
To this point, the present inventors paid attention to a chaos containing whole frequency components and capable of generating a sequence of integers complicated of combination (with a binary code sequence inclusive, and hereinafter called xe2x80x98chaos sequencexe2x80x99), and have carried forward a concentrated research to make use of a chaos sequence for SS signal generation, reaching a new object as mentioned below.
That is, because a desirable binary code sequence for use as an SS signal should be free of inclination between numbers of xe2x80x980xe2x80x99s and xe2x80x981xe2x80x99s, it has come up as an object to be solved how to generate an SS signal in the form of a chaos sequence meeting such a requirement.
The present invention has been made to give solution to the object described and it is an object of the invention to provide a spread spectrum signal generation method and a spread spectrum signal generator which can generate, from a binary code sequence of a chaos sequence, an SS signal free of inclination between numbers of xe2x80x980xe2x80x99s and xe2x80x981xe2x80x99s
Another object of the invention is to provide a stream encryption method which employs a binary code sequence determined by a novel spread spectrum signal generation method disclosed herein, for a stream encryption to be executed to thereby generate a cipher code to be optimum in use, for example, for communications and very high secrecy.
A still another object of the invention is to provide a stream cipher communication method which employs a cipher code, determined by a novel stream encryption method disclosed herein, for stream cipher communications to be performed to thereby implement a stream cipher communication with very high secrecy.
To achieve the object described above, there is provided a spread spectrum signal generation method comprising the steps of: starting an operation by substituting an initial value x(0) to an expression (1), having a resultant value based on an expression (2) again as an input to the expression (1), determining a time series x(t)xe2x88x92t by repeating such operations; and, substituting a quantization resolution n=1 to an expression (3), determining an isomorphic transform and quantization based on the expression (3) in correspondence to the time series x(t)xe2x88x92t, determining a time series y(t)xe2x88x92t from the determined isomorphic transform and quantization, generating a spread spectrum signal having, as a period thereof, a binary code sequence y (t) arbitrary cut out of the time series y(t)xe2x88x92t, where
Logistic mapping: x(t+1)=4x(t){1xe2x88x92x(t)}xe2x80x83xe2x80x83(1),
Feedback: x(t)=x(t+1)xe2x80x83xe2x80x83(2), and
Isomorphic transform and quantization:
y(t)=[{2/xcfx80xc2x7arc sin {square root over (0)}x(t)}xc2x72n]xe2x80x83xe2x80x83(3),
where, t is a discrete time, x(t) is an internal state of a chaos given as a real number with double-precision normalized between xe2x80x980xe2x80x99 and xe2x80x981xe2x80x99, and [ ] is an operator representing a round-off operation of a decimal fraction of a value in the [ ].
According to the invention, there can be provided a concrete method of obtaining, from a logistic mapping as a symmetrical nonlinear mapping and a basic mode (n=1) of a nonlinear quantization observation, multiplicity of binary code sequences free of bias, to generate SS signal which is most suitable in use for CDMA multiple communications.
To achieve the object described above, there is provided a spread spectrum signal generator comprising: a program storage unit for storing a program for execution of operations depending on expressions (1) to (3),
Logistic mapping: x(t+1)=4x(t){1xe2x88x92x(t)}xe2x80x83xe2x80x83(1),
Feedback: x(t)=x(t+1)xe2x80x83xe2x80x83(2), and
Isomorphic transform and quantization:
y(t)=[{2/xcfx80xc2x7arc sin {square root over ( )}x(t)}xc2x72n]xe2x80x83xe2x80x83(3)
where, t is a discrete time, x(t) is an internal state of a chaos given as a real number with double-precision normalized between xe2x80x980xe2x80x99 and xe2x80x981xe2x80x99, and [ ] is an arithmetic operator representing a round-off operation of a decimal fraction of a value in the [ ],
a database for storing a quantization resolution n=1 and an initial value x(0); and
an arithmetic processing unit for starting an operation by substituting to the expression (1) the initial value x(0) stored in the database, having a resultant value based on the expression (2) again as an input to the expression (1), determining a time series x(t)xe2x88x92t by repeating such operations, substituting to the expression (3) the quantization resolution n=1 stored in the database, determining an isomorphic transform and quantization based on the expression (3) in correspondence to the time series x(t)xe2x88x92t, determining a time series y(t)xe2x88x92t from the determined isomorphic transform and quantization, generating a spread spectrum signal having, as a period thereof, a binary code sequence y(t) arbitrarily cut out of the time series y(t)xe2x88x92t.
According to the invention, a spread spectrum signal generator to be implemented in particular as a hardware chip such as a general purpose industrial CPU outputs binary code sequence y(t) determined when the quantization resolution n=1 as spread spectrum signal as necessary.
When the internal state x(t) of chaos ideally including waves having all frequencies is quantized as integer sequence and then observed, 2n combinations of integer sequence is generated in time series where n is a quantizing resolution. At this time, if the observation is performed while a non-liner mapping is linearly quantized, the distribution of integers to be taken out has bias.
On the other hand, logistic mapping: x(t+1)=4x(t){1xe2x88x92x(t)} is an ideal and representative mathematical model of low-division chaos. Isomorphic transform and quantization: y(t)=[{2/xcfx80xc2x7arc sin {square root over ( )}x (t)}xc2x72n] for the logistic mapping generates almost flat distribution of integers from 0 to 2n when long observation is performed, and does not generate a peculiar bias. It is to be noted that, in he expression, [ ] is an arithmetic operator representing a round-off operation of a decimal fraction of a value in the [ ].
In case of random numbers, the frequency distribution appears to be flat when a long and repeated observation is performed. In contrast, in case of a chaos, the distribution variously changes depending on the way of cutting out, because the initial sensibility thereof always remains.
Therefore, according to the present invention, resolution of quantization observation is set to be n=1 and the binary code sequence y(t) is output as binary code sequence as it is, thereby generating a time series which serves as a base for a SS signal. The time series obtained when the calculation of the logistic mapping and the feedback thereof is performed with double-precision depends on the initial value x(0) and has repeatability which is not affected by OS and hardware.
The initial value x(t) is given a real number with double-precision between xe2x80x980xe2x80x99 and xe2x80x981xe2x80x99 except for xe2x80x980xe2x80x99, xe2x80x980.5xe2x80x99 and xe2x80x981xe2x80x99. Therefore, the number of available initial values is equivalent to its precision, i.e. double-precision and thus almost infinite in view of industrial applicability.
There is no limitation with respect to the length of the calculation of the time series. Since there is generated an SS signal having, as a period thereof, binary code sequence y(t) obtained by cutting the time series y(t)xe2x88x92t by a certain length, the kinds of the binary code sequence y(t) are enough.
Further, to achieve the object as described above, there is provided a stream encryption method capable of obtaining enciphered code by performing stream encryption using the binary code sequence obtained by the above spread spectrum signal generation method, wherein the stream encryption is achieved by executing an exclusive OR arithmetic operation on the binary code sequence that has been obtained by the spread spectrum signal generating method according to claim 1 and digital information to be enciphered.
According to the present invention, it is possible to propose a stream encryption method capable of generating ciphered codes with very high secrecy, which is most suitable for using in communication for example.
Further, to achieve the object as described above, there is provided a stream enciphered codes communication method for performing stream enciphered code communication using enciphered codes obtained by the above stream encryption method.
According to the present invention, it is possible to realize the asynchronous multiple multi user stream cipher communication with very high secrecy. More specifically, the invention exhibits extremely excellent effect that the encryption code is generated, enhanced, mixed and converted, and a user having the same spread spectrum signal generator reconstitute this code through synchronization.
It is to be noted that, for the purpose of generating enciphered codes with wider spread and easily perform multiplication, it is preferable to perform calculation with the ratio of the SS signal to digital information of from several times to tens of times instead of 1:1.
When the binary time series {y(t)xe2x88x92t} depending on an initial value is arbitrarily sampled out to prepare many SS signals composed of the binary code sequences y(t) and then stream enciphered codes for digital information are deciphered according to the SS signal, it is possible to perform perfect decryption only by executing synchronized exclusive OR (EXOR) operation.
Further, even when the decryption is asynchronously performed by shifting synchronization of the SS signal, the original text can not be seen or recognized through. Furthermore, even when the original text is English or Japanese sentences composed of ASCII codes and the data spreading ratio is 1, the characters and the words can not be seen or recognized through. The stoutness of encryption is further strengthened when the spreading ratio is selected as from several times to tens of times.
With regard to the safety of the SS signal, the similarity of arrangement of xe2x80x980xe2x80x99 and xe2x80x981xe2x80x99 in an SS signal and the similarity of arrangement of xe2x80x980xe2x80x99 and xe2x80x981xe2x80x99 between SS signals are valued through calculation of auto-correlation coefficients and cross-correlation coefficients. The valuations include not only one for non-similarity in an asynchronous state but also one in a perfect synchronous state.
Any SS signal obtained by cutting a time series generated based on any initial value may be used for spread spectrum communication. The assurance of such independence of the SS signal is derived from or based on the nature of chaos which includes sensitivity for an initial value, impossibility of prediction for a long time, and the divergence and convergence depending on Lyapunovs index.
The nature, principle and utility of the invention will become more apparent from the following detailed description when read in conjunction with the accompanying drawings.